Emblems of Mind: The Inner Life of Music and Mathematics
By Edward Rothstein; Times Books 263 pp., $25
MUSIC and higher mathematics share some obvious kinship. The practice of both requires a lengthy apprenticeship, talent, and no small amount of grace. Both seem to spring from some mysterious part of the imagination, apart from the everyday workings of the mind. Logic and system are essential for both, and yet each can reach a height of creativity beyond the merely mechanical.
Nevertheless, most people find music more understandable than higher mathematics. That is why it is best to approach ''Emblems of Mind: The Inner Life of Music and Mathematics,'' as a work of aesthetics.
Edward Rothstein is chief music critic for the New York Times and also a formally trained mathematician. He writes this book as a foreign correspondent, sending dispatches from a remote and mysterious locale as a guide for the intellectually adventurous. The remarkable fact about his work is not that it is profound, as much of the writing is, but that it is so accessible.
This book is based on a lengthy essay Rothstein wrote for the Times, originally published in 1982. He confides that as a mathematics graduate student, he would be lured away from his studies (algebraic topology, measure theory, nonstandard analysis) by listening to or playing a musical composition. He says that ''music and math together satisfied a kind of abstract 'appetite.' ''
Metaphors are important to his thesis, which is itself based on an elaborate metaphor from the conclusion of Wordsworth's account of his development as a poet in ''The Prelude.''
The poet describes rising in the mist of a summer's night to climb Mt. Snowden in time to see the sun rise from the peak. Rothstein uses this climb as a structure for the work, which is presented as a journey upward, sometimes twisting and turning, but always headed for the final summit of understanding.
The journey alternates between mathematics and music, taking up first one and then the other in order to show the similarities and make sense of the differences. Surprisingly, the chapters of mathematics seem more accessible to the nontechnical reader, perhaps because the author well understands the formidable distance between ''pure'' mathematics and ordinary experience. Unless one has some familiarity with reading a score, the formal musical analyses can be followed only with difficulty.
Rothstein sees the search to define truth in beauty as common to both musicians and mathematicians. Indeed, he raises the question whether truth is possible without beauty. Some of the author's most provocative and exciting speculations surround this question: Is the perception of beauty universal, and if so, is it an infallible guide to truth? He argues that when we perceive beauty in nature, in a musical composition, or in a mathematical formulation, we expect not that everyone will share in our joy, but that they ought to.
Finally then, this work has as its purpose not only to investigate the relations between mathematics and music but also to ask how the understanding of these relations informs the search for meaning.
It is through the study of the creative and the sublime that we can gain a glimpse of this higher order, as Wordsworth has it, ''The perfect image of a mighty Mind,/Of one that feeds upon infinity.'' Although this journey may sometimes seem difficult and beset with stones, Rothstein would have us see that it is filled with joy as well.